Problem: The geometric sequence $(a_i)$ is defined by the formula: $a_i = \dfrac{5}{3} \left(-3\right)^{i - 1}$ What is $a_{3}$, the third term in the sequence?
Solution: From the given formula, we can see that the first term of the sequence is $\dfrac{5}{3}$ and the common ratio is $-3$ To find $a_{3}$ , we can simply substitute $i = 3$ into the given formula. Therefore, the third term is equal to $a_{3} = \dfrac{5}{3} \left(-3\right)^{3 - 1} = 15$.